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Topological Data Analysis in Materials Science: The Case of High-Temperature Cuprate Superconductors

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Abstract—

Adequate formalization of problems is the most important task that has to be solved in order to apply the modern methods of so-called “machine learning” to real problems. The effective application of the metric, logical, regression, and other algorithms of machine learning becomes possible only when feature generation procedures and classes of objects are adequately defined. In this study, the theory of topological analysis of poorly formalized problems and the theory of analysis of labeled graphs were applied to the problem of predicting numerical characteristics of crystalline materials. The methods developed were tested on the problem of predicting the critical temperature of superconducting transition (Tc) of high-temperature cuprate superconductors (1450 structures). As a result, in a tenfold 6 : 1 cross-validation, the best model with a linear recognition operator yielded quite high average value of the correlation coefficient (r = 0.77) between the predicted and experimentally determined values of Tc.

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ACKNOWLEDGMENTS

We are grateful to Prof. O.A. Gromova for useful discussions on expert data analysis.

Funding

This work was supported by the Russian Foundation for Basic Research, project nos. 19-07-00356, 18-07-01022, 17-07-01419, 16-07-01129, and 18-07-00944.

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Authors and Affiliations

  1. Dorodnicyn Computing Centre, Federal Research Center “Informatics and Control,” Russian Academy of Sciences, ul. Vavilova 44, 119333, Moscow, Russia

    I. Yu. Torshin & K. V. Rudakov

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Correspondence to I. Yu. Torshin or K. V. Rudakov.

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Ivan Yur’evich Torshin was born in 1972. He graduated from the Department of Chemistry, Moscow State University, in 1995, received candidates degrees in chemistry in 1997 and in physics and mathematics in 2011. Currently he is an associate professor at Moscow Institute of Physics and Technology, lecturer at the Faculty of Computational Mathematics and Cybernetics, Moscow State University, a senior researcher at the Federal Research Center Computer Science and Control, Russian Academy of Sciences, and a researcher at the Center for Big Data Storage and Analysis, Moscow State University (https://bigdata-msu.ru). He is the author of 485 publications in peer-reviewed journals in informatics, medicine, chemistry, and biology, 9 monographs: 5 in Russian and 4 in English (in the series “Bioinformatics in Post-genomic Era”, Nova Biomedical Publishers, NY, 2006-2009).

Konstantin Vladimirovich Rudakov was born in 1954. He is a Russian mathematician, academician of the Russian Academy of Sciences, Deputy Director of the Federal Research Center Computer Science and Control, Russian Academy of Sciences, Head of Department “Intelligence Systems” at the Moscow Institute of Physics and Technology, and academic advisor at the Center for Big Data Storage and Analysis, Moscow State University.

Translated by I. Nikitin

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Torshin, I.Y., Rudakov, K.V. Topological Data Analysis in Materials Science: The Case of High-Temperature Cuprate Superconductors. Pattern Recognit. Image Anal. 30, 264–276 (2020). https://doi.org/10.1134/S1054661820020157

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